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Introduction to the Discounted Cash Flow Approach

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Introduction to the Discounted Cash Flow Approach 19 CHAPTER THREE INTRODUCTION TO THE DISCOUNTED CASH FLOW APPROACH By Stephen R D’Arcy, FCAS INTRODUCTION The property-liability insurance industry has moved, by choice or otherwise, from a time when there was general agreement on a standard profít margin as a percentage of premium to a time when it is difficult to know what the pro0 margin truly is or should be. That we have not yet arrived at a point where there is a new consensus should be obvious, for then this book would not be necessary. This chapter aims to provide a simple introduction to the concept of discounted cash flow analysis, which is widely accepted in the field of finance as the proper approach in a variety of applications. INSURANCE AND THE CAPITAL MARKETS Assume that you have a significant sum of money available to invest and are considering your altematives. The array of choices includes bonds of differing maturities and credit worthiness, equities with different dividends and price volatilities and an almost unlimited number of other investments in such categories as real estate, futures, and options. In addition, you have the opportunity to underwrite insurance. Viewed in this manner, it seems apparent that you would invest in the insurance business only if the retum on your investment, which would include both underwriting and investment income, were commensurate with the other investment altematives with similar risk characteristics available to you. Although it could be argued that an insurance company does not really make the choice each year about whether to write insurance or instead simply to become an investment fund, that is, in essence, the choice that is being made in the capital markets. If the insurance industry is not eaming a retum high enough to compensate investors with a market leve1 retum (that rate paid on investments with similar risk characteristics), new capital will not be invested in insurance and the capital that can be withdrawn from the insurance industry will be. This trend will continue either until the industry has no capital remaining, an unfortunate possibility for Lloyd’s of London right now, or until the retum improves enough so investors are convinced that a competitive retum will be eamed. Mutual insurance companies may appear to represent an entirely different form of financia1 institution, with a different set of objectives from proprietary insurers. ACTUARIALCONSIDERATIONSREGARDMGRISKANDRETURN 20 However, in essence, mutuals can be viewed as simply a combination contract or tied product, in which an individual’s investment (as owner) and insuring (as policyholder) decisions are made together. If the cost of insurance becomes too high or the retum on investment too low, the mutual will lose its business and its owners. Since the decisions are tied together, though, and the cost of searching for a new insurer and investment may tum out to be higher than searching for a single altemative alone, then the adjustment process to the appropriate leve1 of eamings in a mutual may take longer than in a proprietary insurer. In addition, when a policyholder leaves a mutual company, capital contributed to the firm is, in practice, forfeited. This makes a difference in the investment decision. Also, there is evidente that management in a mutual insurer is less subject to the vicissitudes of a competitive economy than other forms of ownership. Insurance is an extremely complex financia1 transaction, with stochastic payment streams that extend over many years, unique financia1 accounting provisions, a myriad of regulatory requirements, intricate tax regulations, a product susceptible to significant large losses and a market structure unlike any other industry. These factors combine to make it very difficult to measure the retums eamed on the insurance business and the risk characteristics associated with these retums. In light of these difficulties, altemative methods for establishing profit margins are frequently used in the insurance business. To the extent that these models ignore investment income completely, they are fatally flawed, as the insurance business, which in general collects premiums well before losses are paid, functions as a financia1 intermediar-y and invests funds prior to disbursement. The rate of retum eamed on those funds is a vital component of the insurance transaction. To the extent that the altemative models incorporate an historical investment income value, they are usable only as long as the investment markets do not deviate much from their historical levels. In stable financia1 times, interest rates and the market risk premium (the additional retum eamed by investment in a portfolio of equities that reflects the risk characteristics of the stock market as a whole) may remain fairly constant for decades. In that case, the profit margins determined based on historical financia1 values will be reasonably accurate. However, these modek will not be appropriate when signifícant shifts occur in financia1 markets. Given the degree of volatility in interest rates and market retums recently, a model premised on stability is unlikely to be very reliable. In this paper 1 will espouse the use of discounted cash flow analysis to establish the appropriate underwriting profit margins for property-casualty insurance. Discounted cash flow models are one of the forms of financia1 pricing models that combine underwriting and investment retums and also incorporate risk considerations in establishing the target retum on capital figure. Other financia1 pricing models that have been used to establish underwriting profit margins include the Capital Asset Pricing Model and the Option Pricing Model. However, the Discounted Cash Flow approach is more robust than the Capital Asset Pricing Model, since it is not limited to valuing only systematic risk, and more intuitive, with the parameters more easily calculated, than the Option Pricing Model. INTRODUCTION -ro THE DISCOUNTED CASH FLOW APPROACH 21 Essentially, the Discounted Cash Flow approach establishes a floor leve1 for the underwriting profít margin at which the Net Present Value of writing the insurance policy is zero. An insurer would not write a policy if the underwriting profit margin were below that level. In a world of perfect competition and information, the industry underwriting profit margin would converge on that value. However, those assumptions are not necessary for the Discounted Cash Flow approach to be useful. PREsENT VALUE AND NET PRESENT VALUE The Present Value of a series of cash flows is: p&p-- >=I (1 + Y)’ where CF = cash flow t = time r = discount rate The Present Value calculation is generally performed only on the cash inflows from an investment, ignoring the outflows, which are the actual investment made in the project. The Net Present Value calculation considers both the inflows and outflows, and. since most projects require an up-front investment of capital at time zero, the Net Present Value calculation is: When using the Net Present Value decision process, a fírm should invest in a project that has a positive NPV and avoid any negative NPV projects. Thus, when applying the NPV approach to insurance, an insurer should only write a policy if the NPV is greater than zero. The standard criticisms of the NPV approach are that cash flows are uncertain, there may be different views as to the proper discount rate and projects are assumed to be independent. The first two criticisms are assumed to be resolved by the market process. Because cash flows are uncertain, they are discounted at a rate that reflects this uncertainty rather than at the risk-free rate. Although there may be disagreement over the appropriate interest rate to use for discounting, as there are differences in opinion in vaiuing any asset, the market clearing rate, the rate that balances supply and demand, is the rate to use. This assumption works well for widely traded assets, but approximations are needed to value projects that are not publicly traded. The third criticism, that projects are really not independent, is valid. The cash flows included in the valuation of any one ACTUARIAL CONSIDERATIONS REGARDINGRISK AND RETURN 22 project should reflect the impact on other projects as well. However, this is a diffícult task to accomplish. To begin with an overly simplifíed example, in order to focus on the methodology involved in the NPV approach, assume that you have the opportunity to invest SlOO million in insurance for one year. Your $100 million investment will allow you to write $200 million of premiums, on one year policies that are al1 effective the same day, for a line of business that settles al1 claims at the end of one year. Thus, there will be no uneamed premium or loss reserves at the end of the year. The expense ratio on this business will be 25 percent and al1 expenses will be paid when the policies are written. If two further unrealistic assumptions are made, first that the losses are known with certainty, so you assume no risk in writing these policies, and second that al1 capital is invested in risk-free assets, then al1 cash flows can be discounted at the risk-tiee rate. The NPV calculation for this decision is: Npv- s+(s+P(l-m)~f P(l-ER-LR)+S -- + 1 + rf 1 + rr where S = Investment (Surplus) P = Premiums ER = Expense Ratio LR = Loss Ratio 7 = Risk-Free Interest Rate If, for example, this business could be written at a 75 percent loss ratio (including loss adjustment expenses), and the one year risk-free interest rate is 7 percent, then the NPV of this business would be: (100+200(1-.25)).07 2Odl-.25-.75)+ 100 = 981 NPV = -lOO+ + 1.07 1.07 This calculation indicates that the investor would increase the value of his or her holdings by $9.81 million by writing this business.
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